Math homework help by 12pm

Question

Polygraph tests have an accuracy rate of about 95%. This means that it will detect 95% of people who lie and 95% of people who are telling the truth. A company of 4000 employees has everyone submit to a polygraph test. It turns out there are 40 employees who will lie during their polygraph. (Hint: Tests Positive means they are lying!) Complete a table as in your course materials and use it to answer the given question.

If someone does not pass their polygraph test, what is the probability they lied?

(Round your probability to the nearest tenth of a percent!)

Express your answer rounded correctly to the nearest tenth of a percent.

Probability =

Answer 1

40/4000=1/100= 1% Lied

P(L)=.01

P(T)=.99

P(L/Pass)=.05

P(T/Pass)=.95

P(Fail/Lied) = .95

P(L/Fail) =?

P(T/Pass) = .95

use Bayes Theorem

P(L/F)P(F) = P(F/L)P(L)

p(L/F) = P(F/L)P(L)/P(F) = P(F/L).01/.99

P(Lied if you Failed) = P(F/L)(1/99)

P(Lied if you Failed) = .95/99 = .00959595...

= about .01 = about 1.0%